October 25, 1996 11:15 Annual Reviews Frontispiece : Tom Ellison, Alan Front row : S. N. Barua, David Thomas, Bruce Morton, : Ian Nisbet, Harold Grant, Anne Hawk, , Middle row Back row G. I. Taylor with the fluid dynamics “group” in the courtyard of the Cavendish Laboratory, (Spring 1955). Walter Thompson, Owen Phillips, Freddie Bartholomeusz, RogerBill Thorne. Wood, Vivian Hutson, Stewart Turner. Townsend, Sir Geoffrey Taylor, , Fritz Ursell, .

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Annu. Rev. Fluid. Mech. 1997. 29:1–25 Copyright c 1997 by Annual Reviews Inc. All rights reserved

G. I. TAYLOR IN HIS LATER YEARS

J. S. Turner Research School of Earth Sciences, Australian National University, Canberra, A. C. T. 0200, Australia

INTRODUCTION Much has been written about Sir Geoffrey Ingram Taylor since his death in 1975. The greater part of the published material has been written, or strongly influenced, by Professor G. K. Batchelor, who became closer to G. I. Taylor professionally than anyone else had been during his long career. Batchelor (1976a,b; 1986; 1996) has written the definitive obituaries and biographies and earlier edited the collected works, as well as bringing together the rather sparse writings of Taylor about himself and his style of research. The reader may well ask, as the present author did himself on receiving the invitation to write this article: What can anyone else, with far less direct contact, and that contact extending over a shorter period, add to what has already been provided by the acknowledged authority? On reflection, I came to the conclusion that it would be worth recording another perspective on G. I. Taylor, based on the impressions he made on me and some contemporaries who were students in Cambridge from the mid- 1950s onward. We arrived in Cambridge when he was already formally retired from the Royal Society Yarrow Research Professorship, but still very active in research. An informal group of staff and students had by then grown up around him; the theoreticians were members of the faculty of mathematics and the experimenters were in physics, but all of us occupied various spaces in the Cavendish Laboratory. Some of us were directly supervised by G. I. for a time, or collaborated with him on particular projects. (Henceforth in this article I will refer to G. I. Taylor as “G. I.” as he was called by friends and senior colleagues—students at the time addressed him more formally as “Sir Geoffrey”.) Later, in 1966, I returned to Cambridge as a staff member of the Department of Applied Mathematics and Theoretical Physics, which had been established in the interim by George Batchelor (G. K. B.) and contained 1 0066-4189/97/0115-0001$08.00 November 28, 1996 9:23 Annual Reviews chapter-01 AR023-01

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a more formal grouping of mathematicians and experimenters working in fluid mechanics. Over this period too, there was the opportunity to observe G. I. and his interactions with those around him. A second reason for deciding to undertake this task was the opportunity it gives to say some of the things about G. K. B. and his relationship with G. I. which George has never recorded himself. It is widely recognized that G. I.’s effectiveness as a scientist, and the immediacy of his influence on many subjects, was greatly increased by the existence of the group which grew up around him. But the group was largely the creation of George. G. I. was always the “presence” who provided the historical continuity, and also a considerable sense of unity through the pride the group felt in having him in its midst, but he would not have had the interest (or the organizational skills) to bring and hold such a group together himself. My recollections of that period have been stimulated and fleshed out by discussions and correspondence over the past two or three years with many who were my contemporaries in Cambridge at that time. Many of the details recorded below, relating to both G. I.’s scientific work and our personal interactions with him, have been supplied by them, without explicit acknowledgement in the text.

EARLY INFLUENCES ON G. I. TAYLOR’S STYLE OF RESEARCH I shall begin with a necessarily second hand account of some aspects of G. I.’s life, interests, and accomplishments during his boyhood and as a young man. This is highly selective, but I have attempted to pick out events and qualities contributing to the development of the distinctive style of research which has in retrospect been identified as “the spirit of G. I. Taylor.” To concentrate exclu- sively on the post–World War II years of which I have more direct knowledge would, I feel, give a very incomplete and unsatisfactory picture of G. I. and his work. G. I. came from a talented family; it is well known that his grandfather was George Boole, the originator of symbolic logic, who married Mary Everest, the niece of Sir George Everest after whom the world’s highest peak is named. One of the Boole daughters, Alice, became a self-taught mathematician like her father, another a Professor of Chemistry, and the youngest a writer, whose first novel, published in 1897, had a renewed popularity (especially in the U.S.S.R.) after the Second World War. G. I.’s father was an artist, and he grew up in a supportive home with freedom and encouragement to pursue his varied interests. His formal education began at a preparatory school in Hampstead, and his scientific bent seems to have already been formed while he was there. He and November 28, 1996 9:23 Annual Reviews chapter-01 AR023-01

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his younger brother attended the series of Children’s Christmas Lectures at the Royal Institution given in 1897–98 by Sir Oliver Lodge on “The principles of the electric telegraph.” The brothers were stimulated to construct a Wimshurst machine which they used to make X-ray pictures of the bones in their mother’s hand. At the age of twelve G. I. went on to the University College School in Gower Street. He became particularly interested in mathematics and physics, and later acknowledged the influence of the senior mathematics master there. Over the same period, G. I.’s lifelong love of the sea and of small boats began to grow, perhaps prompted initially by his father’s love of rivers, both as a painter and an oarsman. In his last year at school he designed and built a sailing dinghy in his upstairs bedroom, and (having solved the problem of getting it out of the window and lowering it to the ground) sailed it alone down to the mouth of the Thames and back. G. I. is on record as saying that while he was still at school he discovered a copy of Lamb’s Hydrodynamics in his uncle’s library, “and though I could not understand it I was fascinated by its subject matter and hoped that I would some day be able to use it in understanding the mechanics of sailing boats, a subject in which I was already much interested from the practical point of view.” He sculled and rowed while he was an undergraduate in Cambridge, and as soon as he could afford it he bought the first of a series of sailing yachts. When G. I. himself came to give the Royal Institution Children’s lectures in 1936 he chose the title “Ships.” Family influences of various kinds therefore played a great part in develop- ing G. I.’s mind and interests. In his later years he often made the puzzling statement that he saw himself as continuing the family tradition of the gifted amateur, represented by George Everest, George Boole, and his daughter Alice. In conversation it became clear that by this he did not mean to imply an unpro- fessional approach to the work accomplished, but he was stressing instead the image of a relatively untrained person who worked independently and alone for pleasure. He himself was of course far from untrained, but the last two attributes are evident in all his work—he liked doing things himself or with one collaborator or assistant, and he certainly gained enormous pleasure from doing so. In making that statement about the amateur tradition, G. I. probably also had in mind the fact that he continued throughout his life to work with the relatively simple tools he had learned early in his career, rather than mastering new techniques. His unique fresh and original approach more than compen- sated for any lack of new technical skills. In the volume commemorating G. I.’s seventieth birthday, R. V. Southwell (1956) wrote: “From whatever source de- rived, there have always been blended in G. I. the mathematician’s power of abstruse thought and the artist’s gift of perception. Few mathematicians seem to be perceptive—their minds are much too absorbed: G. I., had he felt the November 28, 1996 9:23 Annual Reviews chapter-01 AR023-01

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urge, might have gained a different fame as a field botanist ever quick to note the beautiful and the rare.” G. I. Taylor was awarded a scholarship by Trinity College, and entered Cambridge University in 1905 to study mathematics. He obtained first-class honors in part I of the in 1907 (he was 22nd in his year) and went on to take part II of the Natural Sciences Tripos in physics the next year, again obtaining a first and also a major scholarship at Trinity which allowed him to stay on to do research. After successfully carrying out an experiment on interference fringes at very low light levels, which was suggested to him by J. J. Thomson (and led to his first publication), he won the Smith’s Prize for a theoretical study of the internal structure of shock waves in 1910. This work became his second published paper, and it also gained him a Prize Fellowship at Trinity College, guaranteeing support and freedom to pursue full-time research for six years. A year later he was appointed to a temporary Readership in dynamical mete- orology, established by Professor Schuster, a wealthy physicist at the University of Manchester, to foster more analytical and quantitative studies in that field. He began to work on atmospheric , and made some measurements of the mean and fluctuating wind velocity at various heights above flat ground. This fortuitous change of direction had the important consequence that G. I. was invited to join the Scotia expedition, set up to study icebergs off New- foundland following the Titanic disaster of 1912. The observations he made at that time, using instruments carried by kites and balloons launched from the deck of the sailing ship, were written up in the famous paper “Eddy motion in the atmosphere” (Taylor 1915). This work also exemplifies a characteristic of G. I.’s research which continued throughout his career. In discussions with George Batchelor, G. I. said that “the course of my scientific career has been almost entirely directed by external circumstances” (Batchelor 1975), mean- ing that he did not deliberately choose the most important fields in which to work but simply reacted to events. Within a given field, however, his choice of significant problems and the flair with which he identified and illuminated the essential physical processes were unrivalled. The next major “external event” which influenced G. I.’s research in various ways for many years was the outbreak of World War I. He joined the Royal Aircraft Factory at Farnborough, and in the course of solving very practical and immediate problems set the stage for fundamental advances in both fluid and solid mechanics. He learned to fly in order to gain personal experience of how a plane behaves, and made the first measurements of the pressure distribution over a wing in flight, acting as both the pilot and experimenter. (No doubt he was motivated by the prospect of physical adventure in the open air, an extension of his passion for sailing, as well as by the desire to carry out the November 28, 1996 9:23 Annual Reviews chapter-01 AR023-01

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experiment himself.) During that time at Farnborough, G. I. also analyzed the stress distribution in cylindrical shafts under torsion, when they have a keyway cut in them. He and a colleague studied a soap-film analogue of this geometry, in order to find the effect of rounding the corner, and G. I. began to think about the general problem of the strength of crystalline materials. This later led to the theory of the dislocation mechanism of plastic deformation in crystals, and was the genesis of many of G. I.’s massive contributions to solid mechanics. Though each of these contributions was made in a very practical context, the engineering application of his ideas was never the primary motivation for G. I.’s work. When he had complete freedom to choose his line of research, G. I. was guided simply by curiosity and the excitement of understanding the workings of nature. However, his instinct for choosing the most significant problems in each field he took up, and the elegant way in which he solved them, has meant that this basic work has proved to be of enormous and continuing value in contexts which he could not have foreseen when the work was done. His views are aptly summed up in the final sentences of the article which he wrote for the Annual Review of (Taylor 1974), entitled “The interaction between experiment and theory in fluid mechanics,” which will be referred to in more detail later. He compared his feelings with the intellectual satisfaction expressed by pure mathematicians such as G. H. Hardy. “My feeling is that I derive a rather similar kind of satisfaction from the interplay between applied mathematics and experiment. It is quite a different kind from the satisfaction one gets in doing something useful, though one derives an added pleasure when anything one does turns out accidentally to be of use in engineering.”

RETURN TO CAMBRIDGE, AND RESEARCH BETWEEN THE WARS G. I. returned to Cambridge, and a more normal academic life, in 1919, and he was also elected to the Royal Society in that year. He was a college lecturer at Trinity, implying that he was supported financially by the College and that his duties included undergraduate lectures and supervisions. He was also given a room in the Cavendish Laboratory by Sir Ernest Rutherford, the newly ap- pointed professor. In that room, next to Rutherford’s own, G. I. carried out all his experimental research over the next 35 years. In 1923 G. I. was appointed to one of the two Yarrow Research Professorships of the Royal Society, a position which he held until his retirement in 1951 at the age of sixty-five. During this period his investigations covered a very wide range, and he made seminal con- tributions to many fields of fluid and solid mechanics. The deep significance of some of these studies only became apparent to others many years later. This November 28, 1996 9:23 Annual Reviews chapter-01 AR023-01

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is not the place for an extensive review or even listing of G. I.’s achievements over that time—a broad, but still far from complete, survey is given in the memoir by Batchelor (1976a). Instead of attempting anything of the kind I will just mention and discuss briefly some of the problems tackled by G. I. by his own choice during the years between the wars, and in response to the demands of many government agencies during World War II. These have been chosen mainly because they are related to the themes which were still being actively pursued by the fluid mechanics group in the Cavendish Laboratory in the 1950s, and in the new Department which was established late in that decade. The study of turbulence was foremost among these, and it resulted from G. I.’s returning to problems which he had first thought about in the context of atmospheric turbulence 15 years before. Most of these new contributions were theoretical, but G. I. was influenced by contacts with those making measure- ments in wind tunnels, especially in the Aeronautical Laboratory at Cambridge and at the National Physical Laboratory. The ability to test theories using hot- wire anemometers made this field less abstract and therefore an attractive one to G. I., and his work in the mid-1930s led to the simultaneous publication of four related papers entitled “Statistical theory of turbulence” (Taylor 1935). In these, for the first time, he showed how the velocity and pressure can be described statistically as random functions of time, an approach that is now so standard that the early papers have been absorbed into the subject and are not referred to so often. These papers were also responsible for showing the value of detailed experimental studies of decaying homogeneous and approx- imately isotropic turbulence, downstream of a regular grid of bars in a wind tunnel. The results of these measurements were compared with the predictions of two-point correlation theories, with substantial confirmation of the theoreti- cal results. G. I. introduced the use of Fourier analysis of the spatial distribution of velocity fluctuations, and showed that the Fourier transform of the two-point velocity correlation is the spectral density function representing the different harmonic contributions to the mean-square velocity. The importance of G. I.’s work lay not in the development of new results, but in his novel application of them to the field of turbulence. No discussion of G. I.’s research would be complete without some mention of rotating flows. Working in this field gave him great satisfaction, and he often referred in later years to the experiments he had carried out in the early 1920s (Taylor 1921a, 1922, 1923a). The key result, now called the Taylor- Proudman theorem, is that slow steady motions superposed on a fluid in solid body rotation will be two-dimensional. G. I.’s memorable contributions were his simple laboratory demonstrations of the consequences of this result in various geometries. Patches of dye stirred crudely into a rotating tank of water were November 28, 1996 9:23 Annual Reviews chapter-01 AR023-01

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shown to be aligned in vertical sheets. A solid cylinder of the same density as water, extending through the whole depth and towed horizontally through a rotating tank, moved across a diameter, just as it would in the absence of rotation. A sphere or short cylinder, constrained to move horizontally through a rotating tank of water, carried along the cylinder of fluid above it. The existence of this was demonstrated by placing dye inside the circumscribing cylinder (the dye then moved with the body) or just in front of it when it divided and flowed round the imaginary cylinder as if it were a solid body. This first demonstration of this theoretically predicted but counter-intuitive effect (the “Taylor column”) must have been very exciting indeed. Another extremely influential study in this period was G. I.’s investigation of the stability of circumferential laminar flow of a viscous fluid between coaxial cylinders (Taylor 1923b). In this long and carefully argued paper G. I. calculated the form and stability of the three-dimensional flows satisfying the no-slip boundary conditions and hence predicted both the dimensions and form of the most unstable disturbance and the speed at which it will appear, for a range of relative rotation rates of the two cylinders. He carefully assessed the effect of various approximations, and made detailed calculations using the small gap limit with appropriate corrections. Guided by this theory, he designed apparatus having very long cylinders and a narrow gap to satisfy the strict theoretical conditions. In his subsequent experiments he observed the sudden onset of a periodic array of circumferential cells, with a wavelength almost exactly equal to twice the thickness of the layer of fluid between the cylinders, as predicted by his theory. G. I. summed up the agreement between experiment and theory thus: “...the instability made its appearance at a certain speed in every case when it was expected and in no case when it was not.” This study is in fact historically very important as one of the first successes of linear stability theory in which there was a detailed and convincing comparison between the theory and experiment. It also provided a direct check on the Navier-Stokes equations for a nontrivial flow geometry.

RESEARCH PROJECTS DURING WORLD WAR II During the Second World War, G. I. was much in demand as a consultant on a wide variety of problems in applied classical physics. He was never a committee man by choice, but at that time and later he was willing to serve on strictly technical committees; broader matters of policy were not his forte. Many of the questions he advised on are recorded only in internal reports to various committees and other bodies, though some were followed up in later years and led to journal publications. His major work was concerned with detonation in solids and the resulting blast waves, a field which drew on his November 28, 1996 9:23 Annual Reviews chapter-01 AR023-01

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earlier experience in solid mechanics and shock waves. From measurements of the pressure as a function of time at a given distance from an experimental explosion he was able to deduce the pressure-time relations at other distances, so providing the foundation for the design of structures to resist blast waves. He investigated the properties of spherical shock waves in air, and in a calculation leading to a famous pair of papers on “The formation of a blast wave by a very intense explosion” (Taylor 1950a,b) he simulated the early stages of the atomic bomb explosion cloud. In this calculation the blast was supposed to result from the release of a very large amount of energy at a point source, and a similarity assumption was used, based on the constancy of the total energy of the wave. Comparison of the theoretical results with observations of the initial rate of expansion of the ball of fire leads to an estimate of the total energy or “yield” of the explosion. G. I. was not popular with the US authorities when he deduced an accurate yield from an unclassified publicity film of the 1945 test explosion (which unwisely also showed the elapsed time). Not only did he make the calculations, but he published the results in Proceedings of the Royal Society at a time (1950) when this was still regarded as highly sensitive information which could only be deduced from elaborate ground-based measurements of the pressure and the blast effects of the explosion. During this time G. I. also studied the effects of underwater explosions. Though the pressure round a submerged explosion is nearly spherically sym- metrical, the damage caused to a horizontal steel plate just above the explosion is much greater than it is when a plate is held vertically at the same distance to the side. The explanation of this was clarified by G. I.’s analysis of two effects of gravity. First, the initial gas bubble expands and then it contracts because of the water pressure, before expanding a second time. At the same time it is rising because of its buoyancy and imparting upward momentum to the water around it. At the time of the contraction the momentum is concentrated into a small volume of water, and this produces an intense upward jet which distorts the spherical bubble during the second expansion and does the damage to the solid body above it. G. I., as he always did whenever it was possible, tested this theory through laboratory experiments (carried out with R. M. Davies, and described in an internal report). The work was later followed up by colleagues and students in Cambridge to explain the mechanism of cavitation damage on high speed ship hulls and propellors. Another famous contribution associated with G. I.’s name arose from the observation and interpretation of the surface effect of an underwater explosion. The first phenomenon to be seen is the sudden appearance, then equally sudden disappearance, of an expanding dark circle. Professor Sir William (later Lord) Penney reported discussing this with G. I., who concluded that it must be due November 28, 1996 9:23 Annual Reviews chapter-01 AR023-01

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to an instability, with drops being thrown off the water surface as it is disturbed then returns to its equilibrium position. A few days later G. I. told Penney that he had solved the problem of the behavior of a modulated plane interface between two fluids in a field of acceleration—the original calculation of the Taylor instability. G. I. also contributed to studies of buoyant convection in both oceanic and atmospheric contexts. He was consulted on the feasibility of the bubble-plume concept for damping surface waves approaching a harbor. The surface outflow, produced by a line plume driven by bubbles released from a pipe laid along the bottom, did indeed damp the incoming waves very effectively in a laboratory flume. However G. I. calculated that the power required for a full scale harbor would be prohibitively large, and the idea was shelved. He had earlier made similar calculations on line plumes in the atmosphere to assess their use in temporarily clearing fog from airfields by placing lines of oil burners down each side of a runway. This method was used to good effect in 1942. He also made calculations of the rise of very large plumes in a stratified atmosphere, and of the suddenly released mushroom cloud of an atomic explosion. This work was taken up by G. K. B. and students after the war, and will be discussed in more detail below.

THE IMMEDIATE POSTWAR PERIOD In this section I describe G. I.’s activities and interactions between 1945 and his retirement, a period of which again I have only indirect knowledge, though it was then that the group around him was growing to the strength it had achieved by the time I arrived in Cambridge. At first G. I. concentrated on following up unresolved questions only partly answered in wartime reports, and preparing this work for publication. George Batchelor and Alan Townsend (A. A. T.) arrived in 1945 specifically to become research students under G. I.’s super- vision and to work respectively on theoretical and experimental problems in turbulence, a field in which they had been active at the Aeronautical Research Laboratory in Melbourne during the war. G. K. B. has admitted since that he was somewhat disconcerted to discover that G. I. did not immediately return to the subject of turbulent flow to which he had made such large contributions in the 1930s, though in retrospect he now understands G. I.’s consistent tendency to follow up the most interesting and exciting questions which came to his notice. The research on turbulence was carried on almost independently by these two students, with G. I. showing great interest in their results, but suggesting no specific program for their research. G. K. B. initially followed up Kolmogoroff’s wartime papers on the statistical equilibrium of the small scale components of turbulent motions, and A. A. T. began work on turbulence behind grids in the November 28, 1996 9:23 Annual Reviews chapter-01 AR023-01

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wind tunnel in the Cavendish Laboratory. By 1956 both had published books giving systematic accounts of their own and related research into turbulent flows. Their students in turn worked mainly on problems evolving from this research; those acknowledged in the prefaces to the two books are T. H. Ellison, C. I. H. Nicholl, O. M. Phillips, I. Proudman, P. G. Saffman, and R. W. Stewart. G. I.’s papers written during this period followed up various properties of blast waves and other atmospheric effects of explosions. He also returned for a time to the study of stress waves in solids under high rates of loading. The wartime work on underwater explosions led to a more general study of bubble motions (Davies & Taylor 1950), including the steady rise of large bubbles in unconfined regions and in cylindrical tubes. The phenomenon of the “Taylor instability” on a fluid interface accelerating in the direction of the denser fluid (already mentioned above) was studied in more detail (Taylor 1950c), with the results of experiments carried out by a research student (D. J. Lewis) added to G. I.’s theoretical analysis before publication. At large amplitudes the finger- like disturbances moved with constant velocity into the denser fluid, very like the motion of an air bubble displacing water in a vertical tube. G. K. B. has described (1976) the genesis of the only paper he published with G. I. (Taylor & Batchelor 1949). During both World Wars G. I. had worked on the shape, stability and other properties of parachutes, and had investigated in particular the pressure drop across the fabric for a given rate of flow through it. G. K. B. had been concerned with the aerodynamic effects of sheets of wire gauze used for smoothing the flow in wind tunnels. These two interests came together in a paper presenting calculations of the smoothing effect of a gauze sheet on small steady and unsteady disturbances of the air flow. G. K. B. “found the collaboration difficult, because [G. I.’s] mind worked much more quickly than mine, and if I had not previously invested a good deal of thought in the problem I should not have been able to retain a sense of making an equal contribution.” I feel George was being unduly modest in describing his difficulties in this way, but it is certainly true that G. I.’s individual, instinctive approach to problems and lateral modes of thinking about them made it hard for him to collaborate directly with those around him who were trained, and who reacted, in more conventional ways.

G. I. TAYLOR AS AN EXPERIMENTAL SCIENTIST We now come to the period during which my contemporaries and I were students in Cambridge and formed our direct impressions of G. I. as a scientist. Our views were certainly colored by the knowledge that he was the major living figure in virtually all the fields of fluid mechanics we were learning about and in which we were doing our own research. But his greatness and influence were November 28, 1996 9:23 Annual Reviews chapter-01 AR023-01

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not immediately apparent to the newcomer, and he seemed to have rather little direct interaction with those around him after his retirement. He led by example, and his enthusiasm was evident to all—he liked to show his latest experiments to students and visitors—but by his own choice he was not a dominant leader who sought to have all the younger workers around him pursuing extensions of his own research. Probably he actively did not want others to work on his ideas—he obtained the results he regarded as important himself, and he did not see the point of encouraging others to elaborate on them. G. I. did not have grand ideas about the space and facilities due to him as a great man, and throughout his career he never had a secretary, but wrote his own letters in longhand. In 1954 his office and laboratory in the Cavendish Laboratory had the wind tunnel down one wall (with Fritz Ursell’s desk on the far side, reached by climbing under the wind tunnel), and his own desk was a large cement windowsill, always untidy and covered with letters and papers. The theoretical research students’ desks were next door, all together in a large room which had a pillar in the middle (with a plaque on it recording the fact that on that spot Lord Rayleigh had measured the absolute values of the ohm and the amp). G. K. B had a tiny office off the approach corridor to these rooms, and the other members of staff worked mainly in their Colleges. (The experimental research students who were not working on turbulence were in other odd corners of the Cavendish Laboratory—my lab was in the Old Anatomy Building, and the darkroom was a cellar where they had in previous times stored the bodies awaiting dissection.) G. I. was happiest doing experiments with simple laboratory apparatus, helped by a single technical assistant, who for 40 years (continuing into G. I.’s official retirement) was Walter Thompson. Thompson made all G. I.’s apparatus with great skill, and adapted it to make it do what was required, often starting from minimal written instructions or rough sketches. It was fascinating to listen to the two of them discussing modifications and new possibilities, using a sort of shorthand based on vague references to equipment that had been built years before for a different purpose. The interaction with Thompson was so effective because of the rapid iterations and modifications to a piece of apparatus that could be made with a multi-talented technical assistant standing alongside. The relationship was definitely that of master and servant, strange to those brought up with a more relaxed Australian attitude to such interactions with technical colleagues. G. I. was rather demanding, and sometimes Thompson seemed to be having a stressful time, but he remained loyal and very proud of his position as assistant to a great scientist. Even by the standards of the day and place, G. I.’s equipment was not only simple (and beautifully devised to illuminate the phenomenon being studied) but November 28, 1996 9:23 Annual Reviews chapter-01 AR023-01

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it was often distinctly “low tech.” Sometimes Thompson adapted old apparatus with little regard for safety, and observers at various times noted with some trepidation unprotected high voltage supplies, mercury spilt on the floor, the free use of poisonous chemicals such as carbon tetrachloride and benzene, and so on. Their idea of a speed control for a rotating table was to have Thompson watch a voltmeter and keep the needle on a specified mark by adjusting a rheostat! To the casual observer G. I. was so untidy and messy in the laboratory that he looked clumsy—but the constant stream of elegant results belies that impression. This contrast was never more evident than when G. I. was using a camera. While he appeared to have to recall on every occasion how to use it, the pictures were usually flawless. We can speculate on the extent of the influence of a personal assistant such as Thompson on the success of G. I.’s many experiments. Alan Townsend recalls that G. I. was very skilled with his hands—but was it solely G. I.’s manual dexterity, or partly Thompson’s, which made the experiments work so well, once the apparatus had been built to G. I.’s design? So far I have discussed only the conditions under which G. I. conducted his experimental work; now I turn to the experiments themselves, especially those he carried out after his retirement. The phenomena he studied during those 20 years were diverse, but each piece of research demonstrated, perhaps better than at any time during his career, his intuitive ability to select significant problems and to produce simple, far-reaching solutions to them. He always started with a simple theoretical concept, which he distilled from his own observations of some practical flow, perhaps seen in industry or in the natural world. Another source of ideas was discussion with colleagues (often in another field) who sought his advice about a fluid-dynamical process. He next asked himself how this concept could be given a rational description, without necessarily analyzing all the details of the flow. Then, in his own words (Taylor 1974): “My own method of answering questions of this kind is to think of experiments which depend in the simplest possible way on the concept I have in mind, and then set up apparatus to see whether my preconceived idea is likely to be right.” One often had the feeling that G. I. knew in advance what to expect. In a particular context, quoted by Batchelor (1975), G. I. made a revealing statement that I believe is more generally applicable to his work: “I did not want to publish anything until I found something that could be verified experimentally.” Given the choice between theory and experiments there is no doubt that G. I. preferred being in the laboratory. He adapted his theory to a new case if he saw no easy way to do an experiment to test the original version, always seeking to discover the essence of the experimental observation and reconciling the theory to it. Though he always had a simple, physically based theoretical idea November 28, 1996 9:23 Annual Reviews chapter-01 AR023-01

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in mind, and the interplay between theory and experiment was a vital part of his method of working, he willingly handed on the more complicated and detailed mathematical developments to his younger collaborators. He always chose to stay within the framework of the techniques he had learned as a younger man, and his experiments remained simple because G. I. had the knack of stopping before complications set in. He never thought it worth spending the time learning computer programming, though he used numerical solutions when they were needed to complete a calculation. Probably for similar reasons he did not value highly the more sophisticated elaborations of his initial experiments produced by others, once the phenomena being studied had been explained to his satisfaction. He was interested in principles and concepts, not extra detail just for its own sake. Before going on to record the more personal interactions with G. I., it seems appropriate to discuss in a little more detail several of his later research topics, particularly those in which he collaborated with younger colleagues. I will also mention problems which he personally found especially exciting during that period to illustrate the delight he took in exploring and explaining simple phenomena. Longitudinal Dispersion in Tubes A physiologist asked for help in understanding how drugs are dispersed along the blood vessels of animals. In thinking about this process, idealized initially to the case of laminar flow in a circular tube, G. I. showed that at large distances downstream of the point of injection, the longitudinal spreading of the diffusing material relative to axes moving with the mean speed of the fluid (U) is governed by the diffusion equation. The center of the injected material moves downstream with velocity U and its spread in the flow direction increases as the square root of the distance travelled, and ultimately has a Gaussian distribution. This was immediately interesting because at first sight the situation does not have the corresponding fore-aft symmetry. The mechanism of this dispersion is of fundamental importance in many shear flows. Solute or dye is first dispersed in the direction of flow by advection because the velocity is larger in the center of the pipe. Then molecular diffusion transfers material to the slow-moving fluid near the wall to produce a nearly uniform concentration over the cross section. G. I. showed (Taylor 1953) that the longitudinal diffusivity is a2U 2/48D, where a is the radius of the pipe and D is the molecular diffusivity of the material. This is inversely proportional to D because the lateral diffusion of the solute actually decreases the ability of the shear flow to disperse the material longitudinally. G. I. of course made observations of this process, and also extended the analysis and experiments to turbulent flows in pipes (Taylor 1954). There had been earlier observations in water mains and oil pipelines which showed that

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the position of maximum concentration of an injected tracer moves with the mean velocity, and that the distribution about this is Gaussian, but there was no corresponding theory until G. I. took up the problem. He used the ideas from his paper on “Diffusion by continuous movements” (Taylor 1921b), together with the Reynolds analogy between the lateral transport of heat and momentum in a turbulent flow and an expression for the universal velocity distribution in terms 1/2 of the friction velocity v (0/) , to show that the effective longitudinal = diffusivity is 10 av for both smooth and rough pipe walls. This expression was tested against the published observations on the spread of salt and radioactive tracers in pipe lines and found to be very satisfactory. The publication describing this work (Taylor 1954) also has a section describ- ing careful experiments at the Cavendish Laboratory, made in a long straight pipe fitted with a device for rapidly injecting a slug of salt without disturbing the flow and also with conductivity probes at two positions. Measurements in smooth and rough pipes again agreed well with the theory, but revealed a non- Gaussian distribution at the lower Reynolds numbers used. This was attributed to a thick laminar boundary layer and a slower loss of salt from that layer, so that an asymptotic state was not achieved. The longitudinal dispersion in a curved pipe was shown to be much larger, even though the resistance coefficient was little changed by the amount of curvature used. The measurements just described were made mainly by Dr. T. H. Ellison, a Clare College Research Fellow working with G. I. who designed the apparatus for recording the changes in conductivity. Curiously, G. I. seemed to place little importance on this part of the experimental work, carried out in his own laboratory. He just says, in an acknowledgement to Tom Ellison at the end: “Without his assistance this part of the work would not have been done and I wish to express my thanks to him.”— there was never any question of joint authorship. This, I believe, is a measure of the fact that G. I. already thought his theory had been adequately tested using existing results, and he did not feel comfortable with experiments based on elec- tronic techniques he would not have used personally. A few years later, G. K. Batchelor, A. M. Binnie, and O. M. Phillips made two extensions of this study, to describe the dispersion of neutrally buoyant particles of different sizes, and also slightly buoyant and heavy particles of finite size. The experiments were carried out in a much larger pipe in the Cambridge Engineering Laboratories, but there was by then no thought that G. I. would become directly involved. The Viscous Fingering Instability In following up his work on the finger-like large-amplitude disturbances on an accelerating interface between two inviscid fluids (mentioned above), G. I. deduced, using a theoretical argument, that a similar phenomenon should occur in a porous medium. Strictly, he showed that if a plane interface between two

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fluids moves normally through a porous medium, the interface is unstable to all small disturbances, in the absence of gravity, when the interface moves towards the more viscous fluid. Intuitively he took a further leap forward to suggest that the fastest growing disturbances would form fingers of finite amplitude not only in a porous medium but also in the analogous flow in a Hele-Shaw cell. He tested and confirmed the theory using the latter geometry, while handing over the more detailed calculations of the stability and the shapes of the growing fingers to a postdoctoral collaborator, P. G. Saffman. They published these results jointly in both a conference paper and a journal (Saffman & Taylor 1958). Philip Saffman also published several papers on diffusion in flow through porous media, a problem suggested to him by G. I. following discussions with an oil company, but they never worked together on this problem. The Dynamics of Thin Sheets of Liquids A problem G. I. found especially fascinating was the study of waves on thin liquid sheets, and the breakup of such sheets into drops. [He chose to write about this in the Annual Reviews article already cited (Taylor 1974), stating modestly and inaccurately that it was work he had “taken up more recently because it had seemed amusing rather than because it throws any new light on hydrodynamics”.] He showed theoretically (Taylor 1959) that there are two types of waves controlled by surface tension, an antisymmetrical mode in which the two sides of the sheet move sideways together like a flapping flag, and a symmetrical mode with the two surfaces moving in opposite directions so that the thickness of the sheet varies. The antisymmetric waves move at the same speed for all wavelengths; this speed is (2T/h)1/2, where T is the surface tension, is the fluid density, and h the thickness of the sheet. G. I. carried out experiments in several geometries, using reflected light to make the waves visible. An air jet impinging on a thin sheet of water moving with constant velocity u (and thus constant thickness) produced a stationary antisymmetrical wave confined to the edges of a triangular region and spreading out at a fixed angle from the source consistent with the wave speed. A radially spreading sheet of water produced by directing a jet of water at a disk impactor has a thickness h which is inversely proportional to the radial distance r, and a nearly constant velocity. The angle to the radii at which waves can remain fixed in space is such that sin (Tr/u2)1/2, and the curve with this dependence of angle on distance is a cardioid.∝ A set of cardioids of the predicted scale was indeed produced using an impactor with a regular series of cuts round its circumference. The sheet broke into drops at the radius at which sin 1, where the waves are normal to the radius. In further, more detailed work,= G. I. went on to investigate the size of the drops formed by this disintegration.

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The prediction for antisymmetric waves which G. I. found most interesting is that since wavelets, each of which turns the water sheet through a small angle, can be superposed, it should be possible to set up an experiment in which a thin sheet will turn a sharp corner at a line which is stationary in space. He quickly found the right conditions, which involved interposing a vertical wettable metal sheet in the path of a horizontally spreading sheet of water, close to the impactor. From the points where the edge of the obstructing solid sheet cut the water sheet, two cardioid edges were initiated, enclosing part of the original unobstructed water sheet. The water turned very sharply at this cardioid edge and flowed towards the metal obstruction, so producing a curved, inclined water sheet. The speed of the symmetric waves, on the other hand, depends on the wave- length —i.e. they are dispersive. G. I. showed that they are stationary when inclined at an angle to the flow such that sin (2 2Th/2u2)1/2.He tested this form using a schlieren technique, which is= sensitive to the thickness of the film in transmitted light. A disturbance was introduced by a needle point penetrating the top surface of a radially spreading sheet, and this produced a symmetrical pattern of standing waves, the wavelength of which decreased with increasing angle from the streamline through the needle point, as predicted by the above relationship. Reflected light showed up a co-existing set of cardioid antisymmetric waves, which were invisible in the schlieren pictures. Viscous Fluid Motion with Free Boundaries Several different problems can conveniently be discussed under this heading (which could also include the viscous fingering phenomenon, already described separately above). A fluid advancing into a Hele-Shaw cell does not always completely displace another fluid already filling the cell, and G. I. set out to determine the amount of the original fluid retained by friction at a solid surface (Taylor 1961). The answer, found using careful observations of the amount of viscous liquid left behind in a capillary tube when air is blown in from one end, with of course an associated physical and , is delightfully simple. The fraction of the liquid left behind is a function only of the parameter U/ , where U is the speed of the advancing air, is the surface tension and the fluid viscosity. (This is the only dimensionless combination of the three physical variables.) As this parameter becomes large, the fraction approaches 0.6. This asymptotic value has, however, not been explained theoretically. A related paper (Taylor 1960) considered the deposition of a viscous fluid on a plane surface by a model paint brush or porous roller. G. I.’s simple theory and laboratory experiments were in agreement on the thickness of the liquid layer left on the surface in both cases. The fluid viscosity was shown to be the most important property, though he pointed out the complications due to surface tension in this problem too, and returned to a more detailed study of November 28, 1996 9:23 Annual Reviews chapter-01 AR023-01

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the roller problem in the context of the formation of cavitation bubbles in a hydrodynamically lubricated bearing. A second investigation incorporating some of the same principles, in which G. I. collaborated with A. D. McEwan, is the study of the way in which a flexible strip stuck to a rigid plane surface peels off it when one end is lifted. This is the most detailed and direct collaboration with a younger person I am aware of during this period, and how it came about seems worth recording. At the end of 1963 G. I.’s assistant Walter Thompson had a breakdown and G. K. B. suggested that Angus McEwan, who had begun his PhD research under the supervision of A. A. Townsend, might become a part-time assistant to G. I. in his stead. McEwan declined, but agreed to become G. I.’s student and to work on problems of mutual interest. Technical support was provided by a skilled craftsman, George Garner, who was the sole technician for the several experimenters in the group, including Alan Townsend and G. I. after Thompson’s retirement. Angus has reported that he was a useful go-between for G. I. in the creation and use of equipment, since Garner had other masters to serve, and when G. I. was experimenting constant attendance was necessary. The first problem they worked on together was the peeling strip, and Angus quickly gained G. I.’s confidence by inventing a method of doing this in a con- trolled way in the laboratory. After that, G. I. became a completely sharing collaborator on both the experimental and theoretical aspects of the problem, and the work was published jointly with McEwan as first author. G. I. saw that his own previous understanding of the behavior of the air meniscus ad- vancing into a liquid-filled cavity between separating surfaces allowed them to make a viscous model of a peeling adhesive. McEwan and Taylor (1966) determined theoretically the velocity and stress distributions ahead of the ad- vancing meniscus, and the model experiments showed the formation of fingers on the advancing interface, as observed in practice. The theoretical relation between peeling force and the peeling angle (assumed constant) involves the surface tension except at large values of U/ , and the theory was confirmed by the laboratory measurements. Electrohydrodynamics The last of the major new themes G. I. took up in the years after his retirement began with a more detailed study of the stability of a soap bubble in an electric field, a problem on which he had worked briefly in the 1920s. This led him to the general problem of jets of conducting liquid moving under the influence of an electric field in various geometries. He examined the jets drawn from the free surface of a conducting liquid at the open end of a vertical tube when a potential difference was applied between the liquid and a horizontal plate above the liquid, and showed that the free surface becomes conical as the November 28, 1996 9:23 Annual Reviews chapter-01 AR023-01

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potential difference is increased, and ultimately discharges a jet, with a steady surface shape and inflow into the jet. With Angus McEwan, G. I. examined the stability of a plane interface between a conducting and a non-conducting fluid in the presence of a normal (vertical) electric field (Taylor & McEwan 1965). They showed theoretically that when the field strength exceeds a critical value, which is a function of the surface tension and the density difference, the interface is unstable to small disturbances. The theory predicts the length scale of this instability. Experiments using several pairs of fluids confirmed these predictions. For an air/water interface, fine jets of water are ejected toward the upper electrode (at field strengths smaller than those required to produce sparking due to electrical breakdown of an air layer of the same thickness between solid electrodes).

G. I. TAYLOR AS A SUPERVISOR OF STUDENTS At least in his later years, G. I. did not have an easy relationship with research students. He was more comfortable working and discussing problems with more senior members of the group, and even at the immediate postdoctoral level his reactions were unpredictable; the collaboration with Angus McEwan was a notable exception. Several of the students he supervised at that time only became his students, initially for a couple of terms, when their regular supervisors went on leave (this was true of Bruce Morton, Philip Saffman and myself). This did not guarantee that he would take a detailed interest in their work—Saffman reports having only one half-hour scientific conversation with G. I. during G. K. B.’s absence at Cornell in 1955. Some students who came directly to work with G. I. in fields he had made his own in the past, but was no longer immediately excited about, also got little help. I recall two contemporaries, one working on solid mechanics and the other on rotating flows, who were disappointed about the extent of their interaction with G. I. My own experience was a much more positive one. I arrived as a student in the Cavendish Laboratory, enrolled ahead of time in the meteorological physics group because of my introduction to that field in the CSIRO Cloud Physics group in Sydney. It was not long before I had discovered, through conversations with Owen Phillips (a friend from Sydney University who arrived in Cambridge two years before I did), and with G. K. B., that the fluid mechanics grouping between the physicists and mathematicians was a much more exciting environment in which to work. I transferred to that group, and was initially supervised by Alan Townsend. I began an experimental study of the collision of small drops in a turbulent flow, motivated by my previous interests. This did not get very far, though it led to a joint theoretical paper with Philip Saffman which was later published in the first issue of the Journal of Fluid Mechanics. November 28, 1996 9:23 Annual Reviews chapter-01 AR023-01

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The most important change of direction for me occurred when G. K. B. proposed that I might undertake some laboratory experiments to test the theory of the rise of plumes and “buoyant clouds” in stratified surroundings, which had been developed by his student B. R. Morton. G. K. B.’s starting point was G.I.’s extended entrainment hypothesis, whereby the mean inflow velocity across the edge of a turbulent plume is assumed to be proportional to the mean upflow velocity; he was aware of the wartime report on plumes and clouds in a stratified atmosphere, but not of any subsequent work by G. I. Bruce Morton and I had produced a manuscript documenting the good agreement between theory and experiment, and making predictions for the height of rise in the atmosphere under various conditions, when we discovered that G. I. was also preparing a “much delayed note” on the subject, prompted by a review paper by G. K. B. G. I. was extremely generous to us, and became a co-author on the paper which was, after all, based entirely on his basic idea (Morton, Taylor & Turner 1956). He added a note at the end, explaining the circumstances, and stating “For this reason my name appears with theirs, though I contributed very little to the paper.” He did add some distinctive touches, however; the examples given include estimates of the height of rise of smoke from an autumn bonfire (150 ft) and a burning town (3200 m) with specified burning rates and atmospheric conditions; the mixed units are his! The interaction with G. I. during the writing and publication of this joint paper may give a more general insight into his attitude to his research. Proper recognition of the “ownership” of his ideas was very important to him, and he did regard his publications as a measure of his success. Thus he certainly wished to have his name on the paper, though G. K. B. had a greater direct input into the work and manuscript than he did. Once his seminal contribution was clearly established, however, G. I. did not seek to remain the center of attention. The paper was presented orally at a discussion meeting of the Royal Society by Bruce Morton. G. I. was present and had presumably had a part in organizing the meeting, and could clearly have given the paper himself if he had wished. The other paper presented that afternoon was by R. A. Bagnold, another senior FRS. By the time the experiments on convective plumes and clouds had been completed, G. I. had become my supervisor and he began to think about possible problems for me to work on. He recalled a correspondence with the Chief of the CSIRO Division in which I had worked, Dr E. G. Bowen, whom he had met in Sydney some years earlier. Bowen sent him a series of photographs, which he passed on to me, showing smoke rings formed in certain demolition explosions which maintained their shape as they rose to considerable heights. Bowen was interested in the possibility of using such rings in rain-making experiments to November 28, 1996 9:23 Annual Reviews chapter-01 AR023-01

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project seeding material into clouds, and wrote to G. I. for information about the propagation of vortex rings. G. I. recognized the possible importance of the buoyancy of the fluid in the ring, but had done nothing further. The project was a natural extension of the work on suddenly released buoyant clouds, and I embarked on what was planned to be a mainly experimental study of the phenomenon. G. I.’s style of supervision was always indirect, not detailed, with the implicit attitude: “This is an interesting problem, why don’t you have a go at it.” I was fortunate that his interest in convection had been recently reawakened, so that there was no difficulty in getting his attention on the fairly infrequent occasions when we talked about my work. But his expectations of the likely achievements of research students were not high; when I showed him the theory I had developed to make sense of my experimental results, he looked at the comparison for a while and then exclaimed: “But this is a definite result!” This work led to a paper (Turner 1957) on which G. I. commented helpfully and submitted to Proceedings of the Royal Society for me. When it came to the time of my PhD examination, G. I. was no longer my supervisor, and was eligible to be one of my examiners, with Professor P. A. Sheppard of Imperial College. Their questions during the oral examination were not very probing, and I was left wondering whether they had taken my work seriously; but I later discovered that a similar thing had happened at Owen Phillips’ oral, when G. I. and G. K. B. entered into a long discussion with each other, not with the candidate. G. I. seemed shy with students, as if he did not quite know how to talk with them, either professionally or socially (except when he was showing them an experiment he was currently excited about). The more senior students and young staff members did consult him on occasion about their future careers, and valued his advice. One such piece of advice has been recalled on several occasions. Fritz Ursell asked G. I. whether he should move from Cambridge to Manchester, where he had been offered the Chair of Mathematics. G. I. advised him to accept, though he remarked “whatever decision you make, there will be times when you regret it”! G. I. added that the only decisions he himself had ever regretted were those where he had not taken up opportunities which had been offered. He was always an enthusiasic traveller, and readily accepted invitations to conferences abroad which allowed him (and earlier his wife) to see new places. He blossomed at international meetings, where he enjoyed being the center of attention, while remaining very modest about his work and the many awards he received at such conferences. He was good with young people on these occasions, and many who met him then during his retirement years have pleasant memories of a very approachable and friendly man. November 28, 1996 9:23 Annual Reviews chapter-01 AR023-01

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Lady Taylor was much more sociable and outgoing than G. I., and though they had no children, she was very comfortable with young people. She took an interest in the research students and their families, and gave practical and sympathetic assistance to several of them at times of trouble or bereavement. Many visitors who came to Cambridge to see G. I. were entertained at their home “Farmfield” near Girton. For several years a group party was held there just before Christmas, and all of the contemporaries I have spoken to remember those occasions with pleasure. G. I. rarely reminisced about his life in conversation with younger people, though he wrote several accounts about his family and his own early life and work. He enjoyed talking about sailing, his lifelong hobby, and generally about science and botany in particular—he was very enthusiastic about his garden. He never discussed politics or showed any interest in University or other administration, issues which absorb an increasing fraction of the time for most of us as we grow older. A notable event for those of us in Cambridge at the time was the dinner held in Trinity College to celebrate G. I.’s 70th birthday in March 1956. Research students with some connection with G. I. were invited, with an impressive array of senior friends and colleagues from Britain and further afield. We felt very privileged to be added to a group that included so many famous names, not all of them of course in the field of fluid mechanics.

THE EXTENSION OF G. I. TAYLOR’S INFLUENCE THROUGH THE GROUP IN CAMBRIDGE Finally I will return to a discussion of G. I.’s broader influence on those around him and, through them, the wider dissemination of his ideas and style of re- search. As I have suggested above, he was not a forceful leader seeking to impose his ideas directly on those around him—in fact if it had been left to him, there would have been few such people working near him on related prob- lems, especially after his retirement. The group developed and thrived only because George Batchelor came to Cambridge to work with G. I., and then applied his own talents to nurture fluid mechanics in Cambridge and around the world. G. I. was the powerful figurehead who provided a sense of continuity and a window on the past. We all knew at least something of the vast range of research in fluid mechanics that G. I. had accomplished in Cambridge since he entered this field in 1910, and in conversation he tended to relate what he observed, or was told about, to his past work. His influence was indirect—he led by example and by his mastery of ideas—but his elegance and simplicity, and the way his thinking jumped ahead intuitively, were not easy to communicate to others. November 28, 1996 9:23 Annual Reviews chapter-01 AR023-01

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G. K. B.’s more objective and analytical approach provided a good foil for G. I.’s lateral thinking, and George also brought the organizational and administrative skills needed to attract an increasing stream of talented staff and students to do research in that stimulating environment. But from the beginning, G. I. was certainly an important part of the group—his seminars were highlights, which differed from the generally more mathematical presentations of others. They gave all of us, and perhaps particularly the students working on experiments, a fresh view of the importance of clear, simple physical thinking in choosing and solving problems in fluid mechanics. The informal group of theoreticians and experimenters was small enough, when it began, to fit in the research students’ room for afternoon tea. By 1955 the group had grown to include those shown in the photograph reproduced at the front of this article, and several others. More space was needed, and the wind tunnel and some other pieces of equipment, with the people working on them at the time, were moved to the Balfour Room, a high room in the “new” Austen wing of the Cavendish Laboratory. G. I. also occupied a partitioned-off corner of this room, with his assistant Thompson and later his other collaborators, and while he was active in research, he never moved out of the Balfour Room. By the end of the 1960s G. I.’s rate of working had at last noticeably declined (he was then well over 80), though he continued to meet members of the group after they had moved elsewhere and to come to seminars which interested him. In 1959, G. K. B. succeeded in formally establishing the new Department of Applied Mathematics and Theoretical Physics (DAMTP), grouping together like-minded applied mathematicians from the Faculty of Mathematics and physicists from the Cavendish. This department first acquired more space on the Free School Lane site (adjoining the old and new Cavendish Laboratory buildings) which made it possible to bring most people together. It then moved in 1965 to the old University Press site off Silver St. The proposal to build a fluids laboratory occupying the basement area of the Silver St. building met with strong opposition from both the Physics and Engineering departments. How could a “theoretical” department justify such a facility when much grander laboratories investigating some of the same topics were already in existence elsewhere in the University? But G. K. B. stuck to his guns, insisting on the view engendered by his long association with G. I., that especially in the context of fluid mechanics, applied mathematics is most effective when carried out with a full understanding of the physical phenomena being studied, and ideally in close association with related laboratory experi- ments. His views prevailed, and DAMTP has achieved a growing reputation for physically-based mathematical and experimental research in a number of disciplines, and in fluid mechanics in particular. November 28, 1996 9:23 Annual Reviews chapter-01 AR023-01

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I have no doubt that the style of research which is characteristic of past and current members of DAMTP has been developed directly as a consequence of G. K. B.’s contact with and admiration for G. I.’s way of approaching problems. Those of us who were able to observe G. I. in person, even in his old age, saw that it was possible to investigate significant problems simply and directly, and aspired to bring some of that flair into our own research. One thing I learned very early as a student, and again later as a junior member of staff, was not to try to compete with the awesomely well-trained mathematicians on their own ground—it was possible to make different kinds of contributions which were complementary. The Journal of Fluid Mechanics which G. K. B. started in 1956 also embodies the same philosophy, with a wide range of applications of fluid mechanics and types of papers being represented from the very first issue. Perhaps a “typical” JFM style of paper has emerged, in which theory and a neat laboratory experiment to test it are presented together, though the chief editor has denied that this is a conscious policy! Successive generations of students in DAMTP, and in other laboratories around the world to which their predecessors in the Department have moved, have absorbed a common attitude to fluid mechanics which can be traced back originally to G. I. through G. K. B. Those previously trained as mathematicians do not find it strange that they are expected to do some related experiments, and physicists and engineers begin to think in a different way about theoretical explanations of the phenomena they observe. This seems so natural to many of us now, that we cannot contemplate approaching our research differently, but it is still far from common, and we should remind ourselves of our inheritance, and of the lineage which established our fortune and nourished our progress. Few people have both the ability and the freedom to pursue their research throughout their lives in the unfettered way that G. I. did, and with such out- standing success in identifying and solving problems later recognized to be significant and of wide applicability. But many now appreciate the diverse and not easily defined elements which are embraced by the title of the Symposium held in 1986 in his honor: “Fluid Mechanics in the Spirit of G. I. Taylor.” As we are increasingly being forced into doing more “relevant” and socially useful research (defined in advance by bureaucrats rather than scientists, of course) my own favorite expression of that spirit is contained in G. I.’s last published “dialogue” with George Batchelor (1975). G. I. wrote, in part, “... Idonot see how one can plan a ‘strategy of research in fluid mechanics’ otherwise than by thinking of particular problems. As you say, one may be directed along a particular line by social and political considerations but it seems to me that it is by attention to specific problems rather than by generalized reasoning that advances are made in our subject. I realize that by developing methods of November 28, 1996 9:23 Annual Reviews chapter-01 AR023-01

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analysis which have more general application than to the particular problems which give rise to them, one may facilitate the solution of further problems, but in general it seems to me that it is through particular problems which can be subjected to experimental verification or compared with natural phenomena that most advances are made.”

ACKNOWLEDGMENTS I have greatly enjoyed the conversations with George Batchelor, Angus McEwan, Bruce Morton, Owen Phillips, Philip Saffman and Alan Townsend, during which they shared their memories of G. I. with me. , Michael McIntyre and kindly read the manuscript and made some perceptive comments. Their inputs have increased the breadth and the accuracy of this article, and I am grateful to all of them for their help and interest.

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Ser. A 201:192–96 on the wall of a tube. J. Fluid Mech. 10:161– Taylor GI. 1953. Dispersion of soluble matter in 65 solvent flowing slowly through a tube. Proc. Taylor GI. 1974. The interaction between exper- R. Soc. Lond. Ser. A 219:186–203 iment and theory in fluid mechanics. Annu. Taylor GI. 1954. The dispersion of matter in Rev. Fluid Mech. 6:1–16 turbulent flow through a pipe. Proc. R. Soc. Taylor GI, Batchelor GK. 1949. The effect of Lond. Ser. A 223:446–68 wire gauze on small disturbances in a uni- Taylor GI. 1959. The dynamics of thin sheets of form stream. Q. J. Mech. Appl. Math. 2:1–26 fluid. II. Waves on fluid sheets. Proc. R. Soc. Taylor GI, McEwan AD. 1965. The stability of a Lond. Ser. A 253:296–312 horizontal fluid interface in a vertical electric Taylor GI. 1960. Deposition of a viscous fluid field. J. Fluid Mech. 22:1–15 on a plane surface. J. Fluid Mech. 9:218–24 Turner JS. 1957. Buoyant vortex rings. Proc. R. Taylor GI. 1961. Deposition of a viscous fluid Soc. Lond. Ser. A 239:61–75